A neutron m a s s 1 . 67 × 10 - 27 kg moving at a speed of 1 . 0 × 10 8 ms - 1 collides with a deuteron mass 3 . 34 × 10 - 27 kg at rest and sticks to it. Find the speed of the composite particle triton.

Given: Mass of neutron = 1 . 67 × 10 - 27 kg Speed of neutron = 10 8 m / sec Mass of deuteron = 3 . 34 × 10 - 29 kg Speed of deuteron = 0 Applying law of conservation of momenta m n × v n + m d v d = m n + m d v 1 . 67 × 10 - 27 × 10 8 + 0 = 5 . 01 × 10 - 27 × v ∴ v = 1 . 67 × 10 8 5 . 01 = 3 . 3 × 10 7 m / sec Velocity of combination = 3 . 3 × 10 7 m / sec

A particle of mass 1 . 8 × 10 - 27 kg moving with a speed of 10 6 ms - 1 collides with another particle of mass 3 . 6 × 10 - 27 kg which is initially at rest. The collision is elastic and head-on. Find the speed of each particle after collision.

Given: Mass of the first particle m 1 = 1 . 8 × 10 - 27 kg Initial speed of first particle u 1 = 10 6 m / s Mass of second particle m 2 = 3 . 6 × 10 - 27 kg Initial speed of second particle u 2 = 0 m / s Let the final velocities of two particles be v 1 and v 2 . As the collision is elastic hence kinetic energy and momentum both will remain conserved. Applying law of conservation of momentum: m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2 Putting the values in the above equation we get: 1 . 8 × 10 - 27 × 10 6 + 0 = 1 . 8 × 10 - 27 v 1 + 3 . 6 × 10 - 27 × v 2 10 6 = v 1 + 2 v 2 ....................(i) Applying the law of conservation of kinetic energy, we get: 1 2 m 1 u 2 1 + 1 2 m 2 u 2 2 = 1 2 m 1 v 2 1 + 1 2 m 2 v 2 2 m 1 u 2 1 = m 1 v 2 1 + m 2 v 2 2 1 . 8 × 10 - 27 u 2 1 = 1 . 8 × 10 - 27 v 2 1 + 3 . 6 × 10 - 27 v 2 2 u 2 1 = v 2 1 + 2 v 2 2 ..........................(ii) v 1 = 10 6 - 2 v 2 .....................(iii) Put v 1 in equation (ii) 10 12 = 10 6 - 2 v 2 2 + 2 v 2 2 10 12 = 10 12 + 4 v 2 2 - 4 × 10 6 v 2 + 2 v 2 2 0 = 6 v 2 2 - 4 × 10 6 v 2 or 6 v 2 2 = 4 × 10 6 v 2 v 2 = 2 3 × 10 6 m / s Put v 1 in equation (iii) v 1 = 10 6 - 4 3 × 10 6 v 1 = - 1 3 × 10 6 m / s Hence, first object rebounds back with a velocity = 1 3 × 10 6 m / s , second object starts moving forward with a velocity of 2 3 × 10 6 m / s .

HARD

11th ICSE

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A stationary bomb explodes into $2$ fragments of masses $0.4 kg$ and $4 kg$ . If the bigger fragment has a K.E. of $100 joule$ . Find the kinetic energy of the smaller fragment.

Important Questions on Work, Power and Energy

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11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 10 - Work, Power and Energy>NUMERICALS>Q 33

A neutron

(m a s s 1.67 \times 10^{- 27} kg)

moving at a speed of

1.0 \times 10^{8} {ms}^{- 1}

collides with a deuteron

(mass 3.34 \times 10^{- 27} kg)

at rest and sticks to it. Find the speed of the composite particle triton.

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 10 - Work, Power and Energy>NUMERICALS>Q 34

A $20 kg$ mass which is moving with a speed of $10 {ms}^{- 1}$ strikes a stationary mass of $5 kg$ . After collision the masses stick together. With what speed does the combined mass move?

MEDIUM

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 10 - Work, Power and Energy>NUMERICALS>Q 34

A $20 kg$ mass which is moving with a speed of $10 {ms}^{- 1}$ strikes a stationary mass of $5 kg$ . After collision the masses stick together. What was the kinetic energy of the whole system before the collision?

MEDIUM

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 10 - Work, Power and Energy>NUMERICALS>Q 34

A $20 kg$ mass which is moving with a speed of $10 {ms}^{- 1}$ strikes a stationary mass of $5 kg$ . After collision the masses stick together. What is the kinetic energy after the collision?

MEDIUM

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 10 - Work, Power and Energy>NUMERICALS>Q 34

A $20 kg$ mass which is moving with a speed of $10 {ms}^{- 1}$ strikes a stationary mass of $5 kg$ . After collision the masses stick together. Find the loss in energy after collision. Where has the remaining energy gone?

MEDIUM

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 10 - Work, Power and Energy>NUMERICALS>Q 35

A body of mass

2 kg

moving with a velocity of

3 m / s

collides head-on with a second body of mass

1 kg

coming from the opposite direction with a velocity of

4 m / s

. After the collision, the two bodies stick together. Find the velocity of the stuck bodies.

MEDIUM

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 10 - Work, Power and Energy>NUMERICALS>Q 36

A proton of mass

1.67 \times 10^{- 27} kg

collides elastically head-on with an

α

-particle of mass

6.68 \times 10^{- 27} kg

, initially at rest. After the collision, the

α

-particle moves with a speed of

8 \times 10^{5} {ms}^{- 1}

. Find the speed of the proton before and after the collision.

HARD

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 10 - Work, Power and Energy>NUMERICALS>Q 37

A particle of mass

1.8 \times 10^{- 27} kg

moving with a speed of

10^{6} {ms}^{- 1}

collides with another particle of mass

3.6 \times 10^{- 27} kg

which is initially at rest. The collision is elastic and head-on. Find the speed of each particle after collision.

A stationary bomb explodes into 2 fragments of masses 0.4 kg and 4 kg. If the bigger fragment has a K.E. of 100 joule. Find the kinetic energy of the smaller fragment.

Important Questions on Work, Power and Energy

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A stationary bomb explodes into $2$ fragments of masses $0.4 kg$ and $4 kg$ . If the bigger fragment has a K.E. of $100 joule$ . Find the kinetic energy of the smaller fragment.